On the approximation of smooth functions using generalized digital nets

In this paper, we study an approximation algorithm which firstly approximates certain Walsh coefficients of the function under consideration and consequently uses a Walsh polynomial to approximate the function. A similar approach has previously been used for approximating periodic functions, using lattice rules (and Fourier polynomials), and for approximating functions in Walsh Korobov spaces, using digital nets. Here, the key ingredient is the use of generalized digital nets (which have recently been shown to achieve higher order convergence rates for the integration of smooth functions). This allows us to approximate functions with square integrable mixed partial derivatives of order α>1$\alpha >1$ in each variable. The approximation error is studied in the worst case setting in the _L2$L_2$ norm. We also discuss tractability of our proposed approximation algorithm, investigate its computational complexity, and present numerical examples.     

Numerical investigation of coexisting high and low amplitude responses and safe basin erosion for a coupled linear oscillator and nonlinear absorber system

Over the last half century, numerous nonlinear variants of the tuned mass damper have been developed in order to improve attenuation characteristics. In the present study, the performance of a linear oscillator and an absorber with a strongly nonlinear cubic stiffness is evaluated by using numerical methods. This configuration has been of recent interest due to its capability of wide-band energy absorption. However, high amplitude solutions, which would amplify the response of the system, have been shown to often coexist with the low amplitude solutions. The present research is focused on numerically determining the relative strength of the coexisting solutions. Erosion profiles are presented, quantifying the integrity of the system, i.e. the likelihood of converging to a safe, low amplitude response, and providing an indication of the structural safety of a practical absorber system. The results indicate that the high amplitude solutions not only exist but significantly influence the response of the system within the range of expected operating conditions, particularly at excitation frequencies lower than the natural frequency of the linear oscillator. The erosion profiles indicate a 20–40% increase in system integrity for the case of zero damping compared to a small amount of damping, no significant integrity change when adding a small linear stiffness component to the nonlinear absorber, and no significant change in integrity between the midpoint and extreme of the bi-stable range. Additional higher-period solutions are also discovered and evidence of a chaotic response is presented.     

Peptide-mediated blood-brain barrier transport of polymersomes

A polymeric nanocarrier: Polymersomes tagged with a dodecamer peptide that recognizes gangliosides GM1 and GT1b are shown to cross the blood-brain barrier, both in an in?vitro model and in?vivo. The combination of polymeric vesicles with a small GM1-binding peptide and GM1/GT1b gangliosides as targeting sites for blood-brain barrier transport is unprecedented.     

Thermomolecular orientation of nonpolar fluids

We investigate the response of molecular fluids to temperature gradients. Using nonequilibrium molecular dynamics computer simulations we show that nonpolar diatomic fluids adopt a preferred orientation as a response to a temperature gradient. We find that the magnitude of this thermomolecular orientation effect is proportional to the strength of the temperature gradient and the degree of molecular anisotropy, as defined by the different size or mass of the molecular atomic sites. We show that the preferred orientation of the molecules follows the same trends observed in the Soret effect of binary mixtures. We argue this is a general effect that should be observed in a wide range of length scales.     

Haloalkane dehalogenase catalysed desymmetrisation and tandem kinetic resolution for the preparation of chiral haloalcohols

Six different bacterial haloalkane dehalogenases were recombinantly produced in Escherichia coli, purified, and used to catalyse the conversion of prochiral short-chain dihaloalkanes and a meso dihaloalkane, yielding enantioenriched haloalcohols. A two-reaction one-enzyme process was established in which the desymmetrisation of a dihaloalkane is followed by kinetic resolution of the chiral haloalcohol that is produced in the first step. In case of 1,3-dibromo-2-methylpropane and 1,3-dibromo-2-phenylpropane, an increase of the enantiomeric excess of the respective haloalcohol was observed in time, leading to ee values of >97%, with analytical yields of 24 and 52%, respectively. The results show that haloalkane dehalogenases can be used for the production of highly enantioenriched haloalcohols and that in some cases product enantiopurity can be improved by allowing a two-step one-enzyme tandem reaction.     

Comparison of Two Unsteady Intermittency Models for Bypass Transition Prediction on a Turbine Blade Profile

The present paper evaluates two unsteady transition modelling approaches: the prescribed unsteady intermittency method PUIM, developed at Cambridge University and the dynamic unsteady intermittency method developed at Ghent University. The methods are validated against experimental data for the N3-60 steam turbine stator profile for steady and for unsteady inlet flow conditions. The characteristic features of the test case are moderately high Reynolds number and high inlet turbulence intensity, which causes bypass transition. The tested models rely both on the intermittency parameter and are unsteady approaches. In the prescribed method, the time-dependent intermittency distribution is obtained from integral relations. In the dynamic method, the intermittency distribution follows from time-dependent differential equations. For unsteady computations, self-similar wake profiles are prescribed at the inlet of the computational domain. Joint validation of the prescribed and the dynamic unsteady intermittency models against experimental data shows that both methods are able to reproduce the global features of the periodical evolution of the boundary layer under the influence of a periodically impinging wake. The overall quality of the dynamic method is better than that of the prescribed method.     

Convergent perturbation theory for a q–deformed anharmonic oscillator

A q–deformed anharmonic oscillator is defined within the framework of q–deformed quantum mechanics. It is shown that the Rayleigh–Schr?dinger perturbation series for the bounded spectrum converges to exact eigenstates and eigenvalues, for q close to 1. The radius of convergence becomes zero in the undeformed limit. Received: 6 August 1998 / Published online: 16 September 1998     

Stress distribution in a lap joint under tension-shear

This paper deals with the elastostatic load transfer of a tensile load in a model of an adhesive lap joint (tension-shear problem). The adhesive layer is regarded as infinitesimally thin and the displacement and traction vectors in the adherends are assumed to be continuous across the bond. The problem is reduced to a pair of Fredholm integral equations of the second kind which involve the mean angle between the deformed bond line and the tensile load. This angle, in turn, is determined by means of a scheme due to Goland and Reissner. Numerical results for the bond line stresses and the stress intensity factors at the ends of the bonded region are presented.     

Di‐ and tri‐organotin derivatives of 3S,4S‐3‐[(R)‐1‐(tert‐butyl‐dimethylsilyloxy)ethyl]‐4‐[(R)‐1‐carboxyethyl]‐2‐azetidinone: synthesis,characterization and in vitro antitumour activity

Di‐n‐butyl‐, triphenyl and tri‐n‐butyltin derivatives of 3 S, 4 S ‐3‐[( R )‐1‐(tert‐butyldimethyl‐­<?tw=103.5%>silyloxy)ethyl‐4‐[( R )‐1‐carboxyethyl]‐2‐azetidi<?tw>‐­none were synthesized and characterized. Their antitumour activity was screened against seven tumoural cell lines of human origin. Copyright © 1999 John Wiley & Sons, Ltd.